International Development Secretary Penny Mordaunt and the Leader of the Commons Andrea Leadsom – who, like Ms McVey, both backed Leave in the referendum in 2016 – were also said to harbour deep concerns.

With the negotiations coming to a head, the central focus of the discussions on Thursday is thought to have been the issue of the Northern Ireland “backstop” intended to ensure there is no return of a “hard border” with the Republic.

A number of ministers, including Foreign Secretary Jeremy Hunt, Brexit Secretary Dominic Raab, Environment Secretary Michael Gove and International Trade Secretary Liam Fox, were said to have raised concerns during the meeting which lasted around an hour-and-a-half.

The EU wants Northern Ireland effectively to remain in the single market and the customs union to avoid the need for customs checks until there is a final free trade deal between the UK and the EU.

Mrs May insists such an arrangement must apply to the whole of the UK to avoid the creation of a “border in the Irish Sea” between Northern Ireland and the rest of the UK.

However, Tory Brexiteers fear that she is about to concede to EU demands that it must be open-ended, despite previous assurances from ministers it would have to be time-limited.

Without a time limit, critics say Britain could be tied to the EU indefinitely unable to negotiate free trade deals with other countries. Boris Johnson has said it would reduce the UK to a “permanent EU colony”.

Following three days of talks with key figures in Brussels, DUP leader Arlene Foster – whose party props up the Government at Westminster – issued a renewed warning that they could not accept the EU proposals as they stood.

“The Prime Minister is a unionist. Many of her cabinet colleagues have assured me of their unionism,” she said.

“Therefore, they could not in good conscience recommend a deal which places a trade barrier on United Kingdom businesses moving goods from one part of the Kingdom to another.”